In such a pump one or both end walls are driven into oscillating displacement in a direction substantially perpendicular to the plane of the end wall by an actuator. Where an end wall is so driven, that end-wall surface may, but need not, be itself formed as an element of a composite vibration actuator such as a piezoelectric unimorph or bimorph. Alternatively, the end wall may be formed as a passive material layer driven into oscillation by a separate actuator in force-transmitting relation (e.g. mechanical contact, magnetic or electrostatic) with it.
It is preferable to match the spatial profile of the motion of the driven end wall(s) to the spatial profile of the pressure oscillation in the cavity, a condition described herein as mode-matching. Mode-matching ensures that the work done by the actuator on the fluid in the cavity adds constructively across the driven end-wall surface, enhancing the amplitude of the pressure oscillation in the cavity and delivering high pump efficiency. In a pump which is not mode-matched there may be areas of the end-wall surface in which the work being done by the end-wall on the fluid reduces rather than enhances the amplitude of the pressure oscillation in the fluid within the cavity: the useful work done by the actuator on the fluid is reduced and the pump becomes less efficient.
This problem is demonstrated in the prior art by FIG. 3 of WO2006/111775. FIG. 3A of WO2006/111775 shows a pump in which one end-wall 12 is formed by the lower surface of disc 17 and is excited into vibrational motion by a piezoelectric actuator formed by disc 17 and piezoelectric disc 20. Together, disc 17 and piezoelectric disc 20 form a composite bending-mode actuator whose vibration excites radially-symmetric pressure waves in the fluid within the cavity 11. The amplitude of motion of end-wall 12 is a maximum at the centre of the cavity and a minimum at its edge. A pump incorporating such a composite actuator is relatively simple to construct, as the actuator may be rigidly clamped to the cavity around its perimeter where the amplitude of motion of the actuator is close to zero. However in many practical designs using conventional solid materials for construction of the curved side-walls of the cavity the acoustic impedance of those side-walls is greater than that of the working fluid and consequently the pressure oscillation in the fluid within the cavity will have an antinode at the end-wall. Since, at this location, the side-wall as shown in FIG. 3 of WO2006/111775 has a node, such an arrangement cannot deliver mode-matching that is effective across the full surface area of the end-walls. Indeed, the failure of mode-matching occurs principally at the outer radii of the end-walls, so a substantial area fraction of the end walls and working fluid volume are not vibrationally mode-matched.
FIG. 3B of WO2006/111775 shows a preferable arrangement in which the amplitude of motion of the actuator and therefore of the end-wall 12 approximates a Bessel function and has an antinode at the cavity perimeter. In this case, the driven end wall and the pressure oscillation in the fluid within the cavity are mode-matched, and the efficiency of the pump is improved. However, it is not obvious how such a pump may be constructed, as the actuator must have an antinode of vibration at the side-wall, to which it might normally be mounted.
Two further problems of the prior art are illustrated by FIG. 1 of WO2006/111775, which shows a pump driven by a simple unimorph actuator. The actuator consists of a piezoelectric disc attached to a second disc. If such an actuator is clamped at the cavity perimeter its lowest order mode will be as shown schematically in FIG. 3A.
There are two limitations to this design. Firstly, the thickness and diameter of the piezoelectric disc are determined by the need to achieve the required frequency of vibration and mode-shape in the actuator, effectively fixing the volume of piezoelectric material that may be used. As there is a limit to the power that may be delivered efficiently per unit volume of piezoelectric material, this limitation on piezoelectric disc volume puts a limit on the useful power output of the actuator. Secondly the piezoelectric disc is subject to high strain at its centre, where the amplitude of motion of the actuator and its radius of curvature are highest. It is known that high strains can lead to the degradation of piezoelectric material through its depolarisation, thereby reducing the amplitude of motion of the actuator and thus limiting actuator lifetime. Such high strain at the centre of the actuator may also lead to fatigue of the glue layer between the piezoelectric disc and the second disc if the two are joined by gluing, again leading to reduced actuator lifetime.